As @5n10m stated in comments, you have to push it down (probably about 1/4"), then twist it counterclockwise about a 1/4 turn (if that). There are two pins on the bulb which latch it in place. Considering this is a single filament bulb, the pins will be on the same level. If the bulb is dead already, I wouldn't worry too much about destroying this bulb to get it out.
You'll need to use some penetrant around the base and get the original bulb to move up and down, then you can probably twist it. Once out, you'll want to clean the socket very well to help it not do this again.